1. Field of the Invention
This invention, in general, relates to lens measurement devices and, in particular, to a real-time lens testing system for quickly performing two-dimensional image analyses on a test lens or the like, including the determination of its modulation transfer functions (MTF's).
2. Introduction and Background of the Prior Art
The newest technologies for designing and producing higher quality optical systems of increasing complexity have also created a demand for lens measurement equipment that is sophisticated, flexible, and accurate. In addition, it must be easy to use and be able to provide a rapid indication of the quality of the performance of an optical system compared with its design expectations.
To fulfill such requirements, many branches of science have employed transfer functions which relate output response to a known input as, for example, measuring the performance of audio equipment, vibration isolation, seismology, and so on. As applied to optical systems, the Optical Transfer Function (OTF) has been developed, and it describes the response of optical systems to known sources. It comprises two components: (1) MTF which is the magnitude of the OTF, and (2) the phase transfer function (PTF) which is the phase component. Of most interest here is the MTF.
MTF is a measure of the ability of an optical system to transfer various levels of detail from object to image. Performance is measured in terms of contrast (degrees of gray), or modulation, produced for a perfect source containing the requisite detail.
Detail in an object or image relates to resolution and is customarily specified in line pairs per millimeter (1p/mm). A line pair is one cycle of a light bar and dark bar of equal width and has a contrast of unity where contrast is defined as: EQU Contrast=(Max-Min)/(Max+Min)
where Max is the maximum intensity produced by an image (white) and Min is the minimum intensity (black). Therefore, MTF is a mapping of contrast, measured in percent, against spatial frequency measured in 1p/mm. This mapping is customarily normalized to a value of 1 at zero spatial frequency (all white or black).
One common MTF measurement is that of the eye: the ophthalmologist determines the response of the human visual system (lens and retina) to varying levels of detail--rows of letters. Hence, the doctor determines the frequency response of the patient's visual system.
The Phase Transfer Function (PTF) analogously determines the relative phase of the image as function of frequency. A relative phase change of 180.degree., for example, indicates that black and white in the image are reversed. This phenomenon occurs when the OTF becomes negative. Phase reversed images still show contrast and may have a substantial MTF.
MTF specifications are frequently used for describing the performance expected from lens designs so that actual systems can be repeatably tested to a standard. Some examples of the type of applications for lenses where MTF would be used include reconnaissance lenses, photographic objectives, and IR systems. The benefits of using MTF as a system specification are three-fold. First, many optical systems, other than the very simplest, employ numerous components or stages (lenses, film, eye, etc.) each one of which has associated with it an MTF that can be individually tested and verified. The system MTF is then equal to the product of the MTF's of the individual components. This is referred to as concatenation of MTF and allows for testing at the subassembly level.
Second, MTF, unlike interferometric based measurement, can be specified either at a single wavelength or over a range of wavelengths, depending on the application. Thus, MTF can provide full spectrum specification and testing.
The third benefit of MTF testing is that it is objective and universal. The test engineer is not required to make judgments of contrast, resolution or image quality. Therefore, the polychromatic MTF of an actual lens can be directly compared to the polychromatic MTF as determined by its design under conditions simulating the testing environment or that of another measurement instrument.
Instruments for measuring MTF are also commonly used in production environments as quality control tools because they do not require operators with a high level of optical training to produce meaningful test information indicative of lens performance.
The known fundamental methods for computing MTF include: discrete or continuous frequency generation, opto-mechanical scanning, and wavefront analysis. Recent advancements in precision mechanics and electro-optics technologies have spawned many practical variants of instruments for implementing the fundamental methods to provide for efficient measurement of MTF to very high accuracy.
The most direct test of MTF is to use a single frequency object and measure the contrast of the image directly. Discrete frequency measurement methods are commonplace: bar charts, USAF 1951 resolution targets, and eye charts are but some examples. A series kind of tests taken together can create a full MTF graph.
Improvements over discrete frequency methods involve providing various mechanisms for continuously varying the source frequencies while constantly measuring the image contrast. An example of this approach utilizes a rotating radial grating with a slit aperture as an object. Here, a pinhole is placed in the focal plane of the lens, and the light passing through it is monitored with a detector. As the grating rotates, the individual black and white bars are swept across the pinhole. By moving the grating relative to the slit, the spatial frequencies of the object can be varied. The detector output is synchronized to the rotation and is a direct measure of the MTF at the radial grating spatial frequency and/or its harmonics.
The obvious advantage to frequency generation methods resides in the fact that output is a direct measurement of MTF. The major disadvantage is that these methods require the simultaneous manipulation of sources and detectors, which limits instrument flexibility.
Most commercially available MTF measurement instruments use a form of image scanning. Scanning systems operate on the principles of linear system theory--the image produced by the lens with a known input, such as an infinitesimally small pinhole, is determined, and the MTF is computed from this information.
Measuring MTF with this method is the optical analogy of measuring the frequency response of an audio speaker. The image produced by a lens of an infinitely small source of light is a more or less perfect blur (diffraction or geometric) much like the more or less perfect tonal output of a speaker in response to a single input pulse. The qualities of the blur, its departure from theoretical perfection, similarly indicates the frequency response of the lens.
The image spatial profile is termed the line spread function (LSF) or the point spread function (PSF), for one and two-dimensional scanning. An LSF is commonly produced by edge scanning an image of a point source with a mechanical obscuration (knife edge) while monitoring the intensity throughput, and then differentiating the output. Alternatively, scanned output can be produced by using a slit source and moving a pinhole or slit. The vertical or horizontal orientation of the knife determines whether sagittal or tangential scanning is achieved. If the knife edge possesses a right angle, and it diagonally traverses the image, it can in sequence scan in the horizontal and vertical directions, yielding both sagittal and tangential edge traces. The Fourier transform of the LSF is the one-dimensional MTF.
For a true impulse response function to be derived, a finite source size must be corrected or its state of correction must be taken into account in any subsequent analysis. Through linear system theory, it can be shown that this correction or accounting can be accomplished by dividing the measured MTF by the Fourier transform of the source, such that the corrected MTF data is the quotient of the uncorrected MTF data divided by the proper correction factor at discrete frequencies: EQU MTFcorrected(f)=MTFuncorrected(f)/Correction factor (f)
Computer algorithms can quickly correct measured MTF data for finite aperture sizes (slits, pinholes, etc.). The fully corrected data can then be compared to the theoretical performance.
Through-focus MTF mapping can be generated by opto-mechanically scanning different focus planes. The effects of spherical aberration, defocus, astigmatism, field curvature and chromatic aberration, and other image errors and features can be assessed from these curves. By choosing a single frequency and comparing the MTF at these focal planes, the desired focus for best (or balanced) performance can be achieved.
Very high resolutions (without image magnification) can now be achieved with scanning systems equipped with precision lead screws driven by stepper motors or accurate synchronous motors.
A drawback to opto-mechanical scanning methods is the duration of time to perform the scan. Sampling theory and the lens-under-test parameters dictate the number of data points required for a properly sampled image. Consequently, insufficient sampling can significantly affect the accuracy of the MTF. Therefore, opto-mechanical scans often require upwards of 30 seconds to complete a measurement.
The MTF of a system may also be measured with an interferometer by one of two methods: auto-correlating the pupil function of the lens-under-test or analyzing the PSF calculated by Fourier transforming the pupil wavefrom. This is very convenient for systems which are suitable for testing in an interferometer, do not exhibit significant chromatic aberrations, and whose wavefrom errors do not vary substantially over the wavelength of interest. With opto-mechanical scanning or discrete frequency methods, the wavelength range can be adjusted by using wide band sources and spectral filters for full polychromatic testing. Interferometers rely on monochromatic sources (i.e. lasers) so that MTF is only available at the wavelengths of available sources.
In addition, since phase measuring interferometers have limited wavefront sampling capabilities, the wavefront should be fairly well corrected. Lenses with excessive wavefront errors are difficult to measure with interferometers.
While a variety of instruments have been developed based on the above principles, there is still a need for low-cost, fast, and simple to use instruments for performing image analyses, such as the measurement of the modulation transfer function of optical components and systems, and therefore, it is a primary object of the present invention to provide such an instrument.
It is another object of the present invention to provide an instrument for measuring modulation transfer function in real-time while providing a convenient display of the results.
It is another object of the present invention to provide an instrument for measuring the performance of optical systems by performing real-time, two-dimensional image analysis and displaying the remits through the use of computer system with a graphical user interface.
Yet another object of the invention is to provide versatile and portable apparatus for measuring modulation transfer function.
Other objects of the invention will, in part, appear hereinafter and, in part, be obvious. A full understanding of the invention will be had from the detailed description when read in connection with the accompanying drawings.